A real-time spatiotemporal error compensation framework for face gear grinding

Geometric and thermal errors critically affect the precision of face gear grinding, yet current modeling approaches are computationally intensive and lack real-time adaptability. This study proposes a real-time spatiotemporal error compensation framework for face gear grinding. A closed-loop feedback mechanism is introduced to adaptively update compensation intensity based on residual error feedback, ensuring robustness and efficiency under fluctuating machining conditions. Moreover, a novel spatial-temporal thermal error model is developed by integrating Taylor-graph convolutional network and modified-long short term memory network to capture both node-level spatial fusion and long-term temporal dependencies. High-order terms in geometric error modeling are eliminated using a vector decomposition and truncation-based approach, significantly reducing computational complexity. Furthermore, a high-efficiency multi-source error-tooth flank mapping model is developed based on vector decomposition and truncation function methods, enabling accurate prediction with reduced computational cost. To identify dominant error contributors, an improved Morris-based sensitivity analysis method is integrated, distinguishing geometric and thermal errors affecting tooth flank deviation. Experimental results demonstrate sub-65 ms real-time response, 24.2 μm maximum error reduction, and robust adaptability under fluctuating machining conditions. Compared with recent gear-flank compensation studies, the proposed closed-loop framework achieves a 63.4 % reduction in maximum normal flank error under real machining and <65 ms response latency. This level is comparable to reported reductions based on grid-aggregated metrics in spiral bevel gears (76.82 % reduction of the sum of absolute grid errors), while additionally ensuring real-time, delay-aware execution. These findings validate the proposed system's potential for precision, real-time compensation in multi-axis manufacturing environments.